Express your answer as a mixed number simplified to lowest terms. $13\dfrac{9}{15}-9\dfrac{9}{10} = {?}$
Solution: Simplify each fraction. $= {13\dfrac{3}{5}} - {9\dfrac{9}{10}}$ Find a common denominator for the fractions: $= {13\dfrac{6}{10}}-{9\dfrac{9}{10}}$ Convert ${13\dfrac{6}{10}}$ to ${12 + \dfrac{10}{10} + \dfrac{6}{10}}$ So the problem becomes: ${12\dfrac{16}{10}}-{9\dfrac{9}{10}}$ Separate the whole numbers from the fractional parts: $= {12} + {\dfrac{16}{10}} - {9} - {\dfrac{9}{10}}$ Bring the whole numbers together and the fractions together: $= {12} - {9} + {\dfrac{16}{10}} - {\dfrac{9}{10}}$ Subtract the whole numbers: $=3 + {\dfrac{16}{10}} - {\dfrac{9}{10}}$ Subtract the fractions: $= 3+\dfrac{7}{10}$ Combine the whole and fractional parts into a mixed number: $= 3\dfrac{7}{10}$